BI "Front/Back" vs Cycles "Facing" - Angle of Incidence in Blender Internal
Do these perform the same function and just have different names, or are they doing something different?


No, they don't. They perform something different:


Facing output from Cycles Layer Weight node gives angle of incidence. You can read about this node and how it compares to the Fresnel node here: Relation between Fresnel IOR and Layerweight blend?

You can make it from scratch in Blender Internal node material like this:


Front/Back output from BI Geometry node is the same as Backfacing output from Cycles Geometry node and gives a binary true/false (1/0) if a face is oriented to the camera with it's normal or not.